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題 名 | 二維Holly-Preissmann數值方法的探討與應用於變動飽和地下水污染物傳輸例=Revising of 2D Holly-Preissmann Scheme and Application on Modeling Solute Transport in a Variably Saturated Groundwater Zone |
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作 者 | 許少華; 林伯聰; 倪春發; | 書刊名 | 農業工程學報 |
卷 期 | 48:1 2002.03[民91.03] |
頁 次 | 頁52-63 |
分類號 | 443.67 |
關鍵詞 | 移流; 延散; 二維; 分離演算法; Holly-Preissmann特性線法; Crank-Nicolson法; Advection; Dispersion; Two-dimensional; Split operator; Holly-Preissmann scheme; Characteristics; Crank-Nicolson scheme; |
語 文 | 中文(Chinese) |
中文摘要 | 建構污染物傳輸預測模式,常會遇到嚴重之數值擴散或振盪問題,前人之研究指出其主要源自於移流過程的差分或有限元誤差。本文針對模擬移流過程表現良好之二維Holly-Preissmann特性線法進行研究,先由原理著手,發現為符合其基本假設應進一步進行積分修正,修正後之方法顯示於二維剛體旋轉流場中有優異的表現。將之與模擬延散過程的Crank-Nicolson ADI法以分離演算法結合建構出污染物傳輸模組。水流模組則配合van Genuchten土壤水理曲線,由雙步驟ADI法求解二維Richards方程式。水流與傳輸模組合併成地下水污染物傳輸模式,以不同降雨條件模擬垂直二維土體中污染物於變動飽和層之傳輸現象。研究發現,簡化的平均降雨條件將使數值結果嚴重高估污染物之滲漏深度。 |
英文摘要 | Solute transport modeling usually exhibits spurious damping or oscillation when advetion dominates. Holly-Preissmann scheme for two-dimensional pure advection transport is revised based on its basic theory. Propagation of the second order derivative terms along the characteristic lines is considered in this study by either numerical or analytical integration. The proposed correction is then verified by a benchmark problem with initial distributions of continuous Gaussian in a two-dimensional flow called rigid-body rotation. Split-operator concept is adopted for solving the two-dimensional advection/ dispersion equation. In the first step, only advection process is considered and solved by the Holly-Preissmann scheme. The second step is within the same time interval, in which dispersion operator is performed on the advected resulting distribution. The Crank-Nicolson ADI scheme is used in the dispersion step. A vertical two-dimensional model is then constructed for both flow field and solute transport in variably saturated zone of groundwater. Richards equation and van Genuchten formulas are used as the governing equations for the flow field and solved by two-step ADI scheme to obtain the pressure distribution in the flow field. Unsaturated soil properties are modified at the end of the first step to enlarge the numerical time step. Application of this model shows that the time scale of precipitation can play an important role in predicting the plume movement. Year-averaged precipitation may overestimate the percolation depth of ground pollutant. |
本系統中英文摘要資訊取自各篇刊載內容。